Angle measuring systems have been known in a wide variety of embodiments for many years. They are employed in mechanical and plant engineering and likewise in a wide variety of measuring devices, for example in geodetic devices, coordinate measuring devices or robots. When they are employed, the objective that arises is to determine the angle deviation or corresponding variables derived therefrom, such as velocity or acceleration, for example, between two subsystems rotatable relative to one another in one degree of freedom.
By way of example, such angle measuring systems are used in coordinate measuring devices such as e.g. articulated arms for determining the angle positions in the individual articulations, from which the spatial position of a sensing element fitted to the end of the arm is subsequently calculated.
Such angle measuring devices are also incorporated in geodetic measuring devices, such as a theodolite, for example, which are used to carry out a wide variety of measurement tasks, such as, for example, determining horizontal and vertical angles.
Such angle measuring systems can likewise be found in plants and machines for detecting the positions of machine components such as drives, pivoting heads, throttle valves, rotary tables, and the like. The positions detected in this case can be utilized as position values for measurement purposes, or else for a positioning of components by a drive with a position control loop.
An angle measuring system is constructed from two subsystems movable relative to one another in one degree of freedom. The first subsystem carries a position code, which is detected wholly or partially by a reading head fitted to the second subsystem. By evaluating the signals of the reading head, therefore, an evaluation unit can determine the position of the two subsystems with respect to one another. If the position code is an absolute code, an unambiguous angle position value of the two subsystems with respect to one another can be determined at least in sections. In this case, use is often made of a code table for converting the position code into an angle position value.
A large number of the angle measuring systems available nowadays comprise a plurality of reading heads for determining the angle position values with increased measurement accuracy, for example by reducing the non-systematic errors, such as signal noise, for example, by averaging the individual angle position values. In other applications, a plurality of reading heads can also be utilized for avoiding erroneous measurement values by redundancy.
Owing to the systematic nature of a large number of the errors that occur, the latter are not sufficiently corrected by such averaging. In particular errors which are harmonic with respect to a full revolution, especially low-order harmonic errors such as arise, for example, in the case of rotary encoders as a result of eccentricity, bearing errors, code division errors, etc., in practice often make up a large proportion of the total error. Therefore, it is of particular interest to detect them and correspondingly correct the measurement value. A wide variety of possibilities for calibrating the angle measuring device are known for this purpose.
The calibration of highly accurate angle measuring devices requires extremely high precision calibration apparatuses whose accuracy has to be significantly higher than that of the test specimens to be calibrated. Therefore, such apparatuses are rather complicated to produce and hence cost-intensive. The calibration process is often also associated with very high expenditure of time and labor. It is therefore endeavored to automate this process as far as possible and to dispense with expensive apparatuses.
The publication EP 0 440 833 B1 therefore describes an angle measuring device in which systematic errors are detected and corrected with the aid of a plurality of reading heads, on the basis of a discrete recursive calculation. In this case, for complete correction of the errors over the entire measurement range, owing to the incremental encoding, either a large number of reading heads are required or it is necessary to employ an external reference system which predefines known positions externally. In practice, such a recursive calculation, owing to error propagation and the ever present noise components, also soon encounters limits with regard to the achievable accuracy.
DE 11 2006 003 663 T5 discloses the expansion of the angle errors in a Fourier series, which is particularly suitable for describing and correcting harmonic errors of a rotary encoder over the entire measurement range of 360°. Higher-order harmonic angle errors can be determined accurately with the individual, divided reading head used in that case. Since the small angle covered by the divided reading head is insufficient in the case of the Fourier analysis used for accurately determining low harmonics, it is only by means of a predetermined external positioning of the subsystems with respect to one another that these low-order errors are also made accurately determinable. By way of example, for determining the first harmonic with a Fourier decomposition, measurements at as far as possible opposite positions are advantageous, since said first harmonic can thus be determined to a high proportion and therefore also with a correspondingly good signal-to-noise ratio (see equation 1 below). For this purpose, however, an external reference is necessary in said disclosure, which external reference positions the encoder in predetermined positions in order also to make the low harmonic determinable with sufficient accuracy.
The document EP 1 944 582 A1 discloses a method which, for determining at least one influencing variable that influences the eccentricity in an angle measuring device with a detector arrangement composed of four optical detector elements, a rotatable rotary body with a multiplicity of pattern elements arranged around a pattern center, which are at least partially imaged onto the detector arrangement, resolves the positions and determines the eccentricity of the pattern center relative to a detector center of the detector arrangement. The arrangement of the four detectors used in that case is symmetrical, with a uniform division of the detectors along the circumference of the rotary body, as a result of which, for example, the fourth harmonic cannot be determined.
The document DE 103 57 602 A1 likewise describes an angle sensor in which, during the calibration process, at externally predetermined angle positions, the difference between the measurement value and the externally predetermined angle position is determined and expanded in a Fourier series. The series coefficients are stored and said coefficients, once they have been stored, are used from then on for correcting the measurement values. In that case, too, calibration is possible only with the aid of an external reference.
The article “Self Calibrating Rotary Encoder” by Tsukasa Watanbe et al., which was published in the Journal of Physics, series 13, 2005, on pages 240-245, describes a self-calibrating rotary encoder operating with a plurality of reading heads arranged equidistantly on the circumference.
In the journal “Measurement Science and Technology” issue 19, 2008, R. Probst describes in the article “Self-calibration of divided circles on the basis of a prime factor algorithm” self-calibration of divided circles using a prime factor decomposition for a discrete Fourier transformation.
What is disadvantageous about the known methods is that the error correction, in particular of the low-order harmonic errors, can be determined with sufficient accuracy only with the aid of an externally predefined positioning of the angle measuring system. Consequently, a calibration for reducing these errors is possible only with external aids. This considerably complicates the calibration, particularly after the angle measuring device has been incorporated into a device.
Furthermore, there is also no simple possibility for renewed calibration of the finished device in order, for example, to be able to react to changing ambient conditions or to potential sources of error such as shock and impact stresses, since a highly accurate external positioning of the sensor incorporated in the device is often difficult or even impossible.